Problems of the Supergravity Approximation to String Inflation

Because string theory itself is not very calculable, there are few truly stringy models of cosmology. Therefore, one mostly considers the low energy limit of string theory, supergravity, as an effective field theory, and in this chapter we want to note the problems we encounter when we try to obtain inflation in this effective field theory. As usual, for phenomenological reasons we only consider N= 1 supersymmetry, considering that the rest has been lost at a high scale. In N= 1 supersymmetry, besides the supergravity multiplet, we have the chiral multiplet Φ and the vector multiplet Va.